Method and system for decoupling structural modes to provide consistent control system performance

ABSTRACT

A method and system for calculating a control function for a structural system ( 10 ) that can be used to determine an appropriate control force to apply to an active member ( 18 ) within a stationary member ( 12 ) on the structural system ( 10 ). An active member ( 18 ) and a stationary member ( 12 ) are defined as a two-mass system in which the active member ( 18 ) and the stationary member ( 12 ) move in opposite directions. The stationary member ( 12 ) is mounted to an isolation subsystem ( 14 ) that is composed of six isolators ( 28 ) at multiple degrees of freedom. The isolation subsystem ( 14 ) is softer than the stationary member ( 12 ), active member ( 18 ) and a spacecraft surface ( 16 ) due to a damping element ( 32 ) of the isolation subsystem ( 16 ). The isolation subsystem ( 16 ) is mounted to the spacecraft ( 16 ) and decouples the spacecraft ( 16 ) from the stationary member ( 12 ) and thus the active member ( 18 ). An accurate control force for the active member ( 18 ) can be determined based upon the above structure ( 10 ).

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application is a divisional of and claims priority to U.S.patent application Ser. No. 10/189,860, filed on Jul. 3, 2002, which ishereby incorporated by reference.

FIELD OF THE INVENTION

[0002] The present invention relates generally to methods and systemsfor consistently controlling system dynamics, and more particularly to amethod and system for consistently controlling an active memberconnected to a spacecraft by decoupling the active member from thespacecraft.

DESCRIPTION OF THE RELATED ART

[0003] Conventional methods for modeling active subsystems forspacecraft, such as a reaction wheel subsystem, involve modeling thesystem as two masses in which a first mass is a moving mass, the secondmass is assumed to be ground, and an active control system controls themoving mass. For example, the first mass could be a levitated rotor andthe second mass could be the rotor housing stiffly connected to thespacecraft. However, a problem can occur in the actual hardware of thecontrol system when the spacecraft is not infinitely stiff or aninfinite mass. This can cause instability in the controls and isundesirable.

[0004] This problem often occurs when an actuator commands anelectromagnet to push (or pull) between a suspended rotor and astationary housing to effect levitation. Accurate knowledge of thedynamics and mass properties of the levitated rotor and stationaryhousing as well as the spacecraft to which the stationary housing isattached is necessary to ensure control stability. However, the dynamicsof the spacecraft model rarely fully converge to the dynamics of anactual spacecraft. Even if the dynamics of the spacecraft model arewithin the tolerance range of the actual spacecraft, a control systemdesigned to operate correctly when bolted to one spacecraft may notoperate correctly when bolted to another. In addition, the rotor withinthe suspended housing can transfer disturbance forces to the spacecraft.Such disturbance forces can hinder the control stability of the rotorwithin the suspended housing as well as input undesirable vibrations tothe spacecraft.

[0005] The above-discussed problems are not limited to electromagnets.The disturbance forces and limited control stability can occur in otheractive control systems where mounting structures beyond the actualstationary housing and rotor may cause stability problems. This canoccur when a structural modes and/or spacecraft related disturbancesfall within the bandwidth of the control system. As a result, theconventional methods for modeling space structural systems anddetermining an actuator control system must account for structural(model) characteristics of a variety of spacecraft in determining theforce of an actuator and the control loop for the actuator must bedesigned to react to low frequency disturbances (from the rotor) whilenot reacting to the higher frequency disturbances (from the spacecraft).

SUMMARY OF THE INVENTION

[0006] In view of the above, the present invention provides a method forestimating the dynamics of an active subsystem and determining a controlforce for the active subsystem by decoupling the active subsystem from amounting surface (surface). A structural system is modeled as an activesubsystem mounted to an isolation subsystem that decouples the activesubsystem from a surface. The isolation subsystem decouples the activesubsystem by a plurality (preferably six) of soft highly-dampedisolators that connect the active subsystem to the surface and thatprovide highly damped isolation in-a plurality (preferably six) ofdegrees of freedom. A control loop (in, for example, a microcomputer)commands the actuator to apply a control force to an active memberwithin the active subsystem in order to maintain it at a specificbearing gap. The control force is determined based upon transferfunctions of the active and passive subsystem, without having to takeinto account the dynamics of the surface. An actual structural systemcan subsequently be designed based upon the control force.

[0007] In a second embodiment, the active subsystem is modeled as anarray of interconnected stationary housings. The interconnecting of thestationary housings provides more mass for the actuators to push againstfor maintaining the active members at the bearing gap within the activesubsystem.

[0008] The present invention consequently enables an appropriate controlforce to be determined for application to an active member within astationary housing without having to take into account the dynamiccharacteristics of the mounting surface.

BRIEF DESCRIPTION OF THE DRAWINGS

[0009] Objects and advantages of the present invention will be morereadily apparent from the following detailed description of thepreferred embodiments thereof when taken together with the accompanyingdrawings in which:

[0010]FIG. 1 is an exemplary view of a first embodiment of the presentinvention in which a single stationary housing with an active member ismounted on a surface via an isolation subsystem;

[0011]FIG. 2 is an exemplary view of a D-strut® isolator within theisolation subsystem;

[0012]FIG. 3 is an exemplary view of the first embodiment of the presentinvention in which the single stationary housing is mounted on thesurface via a hexapod of hybrid D-strut® isolators;

[0013]FIG. 4 is an exemplary view of a second embodiment of the presentinvention in which an array of interconnected stationary housings ismounted on a surface via an isolation subsystem;

[0014]FIG. 5 is a flow diagram of the methodology of the presentinvention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0015] In overview form the present disclosure concerns structuralsystems designed for space travel. Examples of such systems includespacecraft that carry rotor housings. As further discussed below variousinventive principles and combinations thereof are advantageouslyemployed to determine a control vector force to be applied by anactuator within the rotor housing and to decouple the rotor housing fromthe spacecraft.

[0016] The instant disclosure is provided to further explain in anenabling fashion the best modes of performing the embodiments of thepresent invention. The disclosure is further offered to enhance anunderstanding and appreciation for the inventive principles andadvantages thereof, rather than to limit in any manner the invention.The invention is defined solely by the appended claims including anyamendments made during the pendency of this application and allequivalents of those claims as issued.

[0017] It is further understood that the use of relational terms such asfirst and second, top and bottom, and the like, if any, are used solelyto distinguish one from another entity, item, or action withoutnecessarily requiring or implying any actual such relationship or orderbetween such entities, items or actions. Much of the inventivefunctionality and many of the inventive principles are best implementedwith or in software programs or instructions. It is expected that one ofordinary skill, notwithstanding possibly significant effort and manydesign choices motivated by, for example, available time, currenttechnology, and economic considerations, when guided by the concepts andprinciples disclosed herein will be readily capable of generating suchsoftware instructions and programs with minimal experimentation.Therefore, further discussion of such software, if any, will be limitedin the interest of brevity and minimization of any risk of obscuring theprinciples and concepts in accordance with the present invention.

[0018] The present disclosure will discuss various embodiments inaccordance with the invention. The system diagrams of FIGS. 1-4 will beused to lay the groundwork for a deeper understanding of the presentinvention and advantages thereof. FIG. 1 in large part and at thesimplified level depicted is a representative diagram of a structuralsystem (system) 10 and will serve to explain the problems and certaininventive solutions thereto according to-the present invention.

[0019] Referring now to the drawings in which like numerals referencelike items, FIG. 1 shows an exemplary system 10 in which a firstembodiment of the present invention is implemented. Specifically, thesystem 10 includes a stationary housing 12, an isolation subsystem 14and a mounting surface such as, for example, a spacecraft surface 16.The isolation subsystem 14 mounts the stationary housing 12 to thespacecraft surface 16. The stationary housing 12 and the isolationsubsystem 14 will be discussed in detail below.

[0020] The stationary housing 12 includes an active member 18 within thestationary housing 12, a control member 20 for controlling the activemember 18 and at least one bearing gap sensor 21. The active member 18may be, for example, a rotor 18 that is magnetically levitated to apredetermined position within the stationary housing 12. The controlmember 20 may be, for example, an actuator 20 that controls a set ofelectromagnets 22 a, 22 b. The rotor 18 is positioned a predetermineddistance within the stationary housing 12. This predetermined distanceis referred to as a bearing gap x. Structural modes or randomdisturbances from the spacecraft often cause the rotor 18 to becomedisplaced from the bearing gap x. The bearing gap sensor 21 measures theposition of the rotor 18. The actuator 20 maintains the rotor 18 at thebearing gap x by applying a control vector force u to the electromagnets22 a, 22 b. A control device (not shown) such as, for example, amicrocomputer or analog control device including a closed loop controlcommands the actuator 20. If the bearing gap sensor 21 determines thatthe rotor 18 is displaced from the bearing gap, the electromagnets 22 a,22 b can increase the control force based on the measurement of thebearing gap. More specifically, the actuator 20 applies a current to theelectromagnets 22 a through wire coils 24. Each of the electromagnets 22pulls on an iron trunnion 26 of the rotor 18 at a plurality of degreesof freedom with the control vector force u to maintain the rotor 18 atthe bearing gap, if the current is positive. The electromagnets 22 bpull on the iron trunnion 26 in a similar manner if the current isnegative. For example, in FIG. 1, the electromagnets 22 apply forces inthe x direction (Fx) for maintaining the rotor 18 at the bearing gap x.

[0021] Referring to FIG. 2, the isolation subsystem 14 mounts thestationary housing 12 to the spacecraft surface 16, and is secured toboth the stationary housing 12 and the spacecraft surface 16 by, forexample, bolts (not shown). The isolation subsystem 14 includes aplurality of isolators 28, each at a respective degree of freedombetween the stationary housing 12 and the spacecraft surface 16.Preferably, the isolation subsystem 14 includes at least six isolators28. Only one isolator 28 is shown in FIG. 2 for ease of illustration.The isolator 28 is preferably a D-strut® that is disclosed in U.S. Pat.No. 5,332,070, which is hereby incorporated by reference. Otherisolators, such as springs, may be utilized. However, the D-strut®provides faster roll off and higher damping. The D-strut® isolator 28includes a primary spring 30 in parallel with a series damper element 32and secondary stiffness element 34. The spring element 30 makes theisolator 28 softer than the stationary housing 12 and the spacecraftsurface 16. The softness of the isolator 28 prevents communication ofspacecraft structural modes and reduces disturbance forces from thestationary housing 12 and the rotor 18 from reaching the spacecraftsurface 16. Such disturbance forces can cause jitter, image blurring(when, for example, the spacecraft is carrying an optics payload), orcan excite lightly damped structural modes on the spacecraft if thedisturbance forces reach the spacecraft surface 16. However, thespacecraft has to communicate attitude control forces to the actuator 20to maintain the spacecraft at a certain attitude. These attitude controlforces occur at relatively lower frequencies than the disturbanceforces. The primary spring 30 and the secondary stiffness element 34maintain the isolators 28 at a level of stiffness sufficient to permitcommunication of the low frequency attitude control forces while thedamper element 32 provides enough softness to prevent communication ofthe high frequency disturbance forces.

[0022] The isolation subsystem 14 also prevents spacecraft disturbanceforces from contributing to the displacement of the rotor 18 within thestationary housing 12 if the structural modes of the spacecraft aregreater than those in the isolation subsystem 14. As a result, thecontrol vector force u applied by the electromagnets 22 can bedetermined without having to take into account the structural responseof the of the spacecraft surface 16 to the rotor control forces. Therelationship between the control vector force (u), the velocity ofdisplacement of the bearing gap (y), the transfer function of the rotor18 (Y^(R) _(y)), and the transfer function of the stationary housing 12(Y^(H) _(y)) is shown by formula (1):

y/u=−ΣY ^(R) _(y) +ΣY ^(H) _(y)   (1)

[0023] The transfer functions of the rotor Y^(R) _(y) and the stationaryhousing Y^(H) _(y) can be determined by process testing. For example, atest force F could be applied to the rotor 18 and to the stationaryhousing 12 by a vibration driver at points in which they interface withthe bearings 22, and by detecting a velocity of the rotor V_(R) and thestationary housing V_(H) by a vibration sensor in response to the testforce. The relationship between the velocity and the test force is shownby formulas (2) and (3).

Y ^(R) _(y) =F/V _(R)   (2)

Y ^(H) _(y) =F/V _(H)   (3)

[0024] As shown by formula (1), the transfer functions of the isolationsubsystem 14 and the spacecraft surface 16 do not affect the bearing gapvelocity or the control vector force that is needed to correct thebearing gap velocity. Specifically, the isolation subsystem 14 decouplesthe spacecraft surface 16 from the stationary housing 12. As a result, amodel for the stationary housing 14 and the rotor 12 can be utilized toaccurately determine the actuator 20 and control force that is neededwithout having to take into account the transfer functions of thespacecraft surface 16 or isolation subsystem 14.

[0025] Referring now to FIG. 3, the stationary housing 12 mayalternatively be mounted to the spacecraft surface 16 via a hexapod ofhybrid D-struts® 38. The hybrid D-strut® is disclosed in U.S. Pat. No.6,003,849 and is incorporated herein by reference. The hexapod of hybridD-struts 38 mounts the stationary housing 12 to the spacecraft surface16 at six degrees of freedom via six hybrid D-struts 39. Each hybridD-strut® 39 includes voice coils on the stroke with an open loop feedforward control. The voice coils can be commanded to communicate theattitude force from spacecraft surface 16 to the stationary housing 12if the attitude of the spacecraft must be adjusted.

[0026] Referring now to FIG. 4, a second embodiment of the presentinvention will now be discussed. A plurality of stationary housings 40,each with a respective rotor 18 and a respective set of electromagnets22, is interconnected as an array of N stationary housings 40 mounted onthe spacecraft surface 16 via the isolation subsystem 14. The stationaryhousings 40 are relatively light in weight in comparison to the rotors18. As discussed above, the electromagnets 22 apply a control vectorforce by pushing or pulling on the trunnion 26. However, theelectromagnets 22 also apply an opposite vector force to the stationaryhousing 12 while applying the control vector force to the trunnion 26. Asingle stationary housing 12 may not provide sufficient mass for theelectromagnets 18 to push or pull against. Therefore, by interconnectingthe system 10 with an array of stationary housings 40, each of theelectromagnets 22 will have sufficient mass to push or pull against. Theisolation subsystem 14 prevents disturbance forces due to, for example,ripple or rotor imbalance as discussed above. The control force [F₁, F₂,F₃ . . . F_(N)] to be applied by each respective magnetic bearing 18 isdetermined in accordance with Formula (1) for each of the array ofstationary housings 40 and each corresponding rotor 18. Time domain orother excitation and sensing methods could be used rather than thetransfer function measurements resulting from the test forces. Takingappropriate averages of the measurements using Fourier transforms couldthen create the transfer functions.

[0027] Two primary conditions must be satisfied for determining anaccurate control force. A bandwidth of the active member 18 must be lessthat the break frequency of the isolation subsystem 14 by apredetermined ratio and the structural modes of the mounting surface 16must be greater than the structural modes of the isolation subsystem 14also by the predetermined ratio. The predetermined ratio depends on thetype of isolation subsystem 14. For example, if the isolation subsystem14 includes a plurality of D-struts®, the predetermined ratio is four.Therefore, the structural modes of the mounting surface 16 would have tobe four times greater than the structural mode of the plurality ofD-struts®. However, the predetermined ratio could be eight or higher fora non-D-strut® isolation subsystem 14.

[0028] The methodology of the present invention will now be discussedwith reference to the exemplary system 10 of FIG. 1 and the flow diagramof FIG. 5. At 52, the stationary housing 12, the rotor 18 within thestationary housing 12 and the actuator 22 are modeled as a two masssystem in which an inner active member, such as the rotor 18, moves in adirection opposite from an outer housing, such as the stationary housing12, and a control force is applied between the inner active member andthe outer housing. The model could be designed by, for example, asoftware simulation package. At 54, it is determined whether the system10 includes more than one stationary housing 12. If the system 10includes more than one stationary housing 12, at 56 a plurality ofstationary housings are modeled as an array of stationary housings (suchas stationary housings 40 shown in FIG. 4). The array of stationaryhousings 40 can be modeled as being, for example, bolted together. At58, transfer functions are determined for all stationary housing models12 and each rotor model 18 within the stationary housing at all degreesof freedom in which the control force would be applied (the axes of thecontrol force vector). At 60, the control vector force is determined byapplying Formula (1) for each axis to limit the velocity of displacementof each rotor 18 (modeled as an inner active member). The stationaryhousing 12 (or array of stationary housings 40) is then mounted on anisolation subsystem 14 such as, for example, the D-struts 28 at sixdegrees of freedom. Conventional control methods can then be used tooptimize system controls based upon the determined control vector force.

[0029] The methodology of the present invention is not limited to thesystem 10 that includes the spacecraft surface 16 or the rotor 18. Thepresent invention could be applied to any system involving two masses inwhich the first mass is freely suspended, the second mass is essentiallyground and an active control system controls the freely suspended mass.Another example of such a system is an array of energy wheels mounted toa spacecraft for providing energy storage.

[0030] While the above description is of the preferred embodiment of thepresent invention, it should be appreciated that the invention may bemodified, altered, or varied without deviating from the scope and fairmeaning of the following claims.

1. A structural system comprising: a stationary housing that includes arotating member positioned at a predetermined bearing gap within thestationary housing; an actuator that repositions the rotating member atthe predetermined bearing gap within the stationary housing if therotating member is displaced from the predetermined bearing gap; and anisolation subsystem that connects the stationary housing with aspacecraft, wherein the isolation subsystem is softer than thestationary housing and the spacecraft, and substantially limitscommunication of disturbance forces from the stationary housing to thespacecraft and from the rotating member to the spacecraft.
 2. Thestructural system of claim 1, wherein the isolation subsystemsubstantially limits disturbance forces that occur at frequencies higherthan a predetermined rate from communicating with the actuator.
 3. Thestructural system of claim 2, wherein the actuator repositions therotating member at the predetermined bearing gap by applying a forcevector to the rotating member that is determined in accordance with atransfer function formula as follows: y/u=−Y ^(R) _(y) *u+Y ^(H) _(y)*u,wherein y represents a velocity of the displacement of the rotatingmember from the predetermined bearing gap, u represents the forcevector, Y^(R) _(y) represents transfer functions of the rotating memberat respective degrees of freedom, and Y^(H) _(y) represents transferfunction of the stationary housing at a respective degree of freedom. 4.The structural system of claim 1, further comprising: an array ofstationary housings, each stationary housing in the array of stationaryhousings including a rotating member that is positioned at apredetermined bearing gap; an actuator within each stationary housing inthe array of stationary housings that repositions the respectiverotating member at the predetermined bearing gap within the stationaryhousing if the rotating member is displaced from the predeterminedbearing gap; and wherein the isolation subsystem connects the array ofstationary housings with a spacecraft, the isolation subsystem is softerthan the array of stationary housings and the spacecraft, andsubstantially limits structural communication from the array ofstationary housing to the spacecraft and from the rotating member to thespacecraft.
 5. The structural system of claim 4, wherein the isolationsubsystem includes a plurality of isolators each at a specific degree offreedom between the outer housing and the spacecraft.
 6. The structuralsystem of claim 4, wherein the isolation subsystem comprises a hexapodof hybrid D-struts, each hybrid D-strut at a specific degree of freedombetween the outer housing and the spacecraft.
 7. The structural systemof claim 4, wherein each of the actuators repositions the respectiverotating member at the predetermined bearing gap by applying a forcevector to the rotating member that is determined in accordance with asystem transfer function formula as follows: y/u=−ΣY ^(R) _(y)*u+ΣY^(H)_(y)*u, wherein y represents a velocity of the displacement of therotating member from the predetermined bearing gap, u represents theforce vector, Y^(R) _(y) represents a sum of the transfer functions ofthe rotating member at respective degrees of freedom, and Y^(H) _(y)represents a sum of the transfer functions of the stationary housing ata respective degrees of freedom.
 8. The structural system of claim 4,wherein the isolation subsystem includes a plurality of D-struts each ata specific degree of freedom between the outer housing and thespacecraft.
 9. The structural system of claim 4, wherein the isolationsubsystem comprises a hexapod of hybrid D-struts, each being located atspecific degree of freedom between the outer housing and the spacecraft.10. A method of estimating dynamics of a structural system, comprising:interconnecting a plurality of subsystems together as a housingsubsystem; mounting the housing subsystem on an isolation subsystem atone or more degrees of freedom for isolating the housing subsystem froma surface subsystem; determining one or more transfer functions ofinterest for the housing subsystem mounted on the isolation subsystem ata plurality of degrees of freedom; and creating a control force transferfunction based on the determining of the one or more transfer functionsof interest.
 11. The method of claim 10, wherein the mounting of thehousing subsystem on an isolation subsystem at a plurality of degrees offreedom for isolating the housing subsystem from a surface subsystemfurther comprises mounting the housing subsystem on a hexapod of hybridD-struts that is connected to the surface subsystem.
 12. The method ofclaim 10, wherein the interconnecting of the plurality of subsystemstogether as the housing subsystem further comprises defining the housingsubsystem as a two-mass subsystem where an active member within thehousing subsystem moves in a direction opposite that of an outer housingmember of the housing subsystem, and positioning the active member at apredetermined displacement relative to the outer housing.
 13. The methodof claim 12, wherein the determining of one or more transfer functionsof interest for the housing subsystem subsequent to the mounting of thehousing subsystem on the isolation subsystem at a plurality of degreesof freedom further comprises determining a transfer function of theactive member and a transfer function of the outer housing member. 14.The method of claim 13, wherein the creating of a control force transferfunction based on the determining of one or more transfer functions ofinterest further comprises creating a performance transfer function byapplying a transfer function formula for all determined transferfunctions of the active member and the outer housing as follows: y/u=Y^(R) _(y) *u−Y ^(H) _(y) *u, wherein y represents an output velocity, urepresents a control force, Y^(R) _(y) represents an active membertransfer function and Y^(H) _(y) represents an outer housing membertransfer function.
 15. The method of claim 14, wherein the creating of asystem performance transfer function based on the determining of one ormore transfer functions of interest further comprises creating aperformance transfer function by applying a system transfer function forall determined transfer functions of the active member and the outerhousing as follows: y/u=−ΣY ^(R) _(y) *u+ΣY ^(H) _(y) *u, wherein yrepresents an output velocity, u represents a control force, ΣY^(R) _(y)represents a sum of active member transfer functions at respectivedegrees of freedom, ΣY^(H) _(y) represents a sum of housing membertransfer functions at respective degrees of freedom.
 16. A method ofoptimizing performance of a control system comprising: interconnecting aplurality of rotor housings that each include a rotor and an actuatorbetween the rotor and the rotor housing as one rotor housing; connectingthe one rotor housing to a spacecraft by mounting the one rotor housingto an isolation subsystem at all axes of structural communicationbetween the one rotor housing and the isolation subsystem whilepreventing structural communication from the one rotor housing to thespacecraft; and determining an actuator transfer function for eachactuator of the plurality of rotor housings by applying a systemtransfer function formula to all transfer functions of the plurality ofrotor housings at all degrees of freedom as follows: y/u=−ΣY ^(R) _(y)*u+ΣY ^(H) _(y) *u, wherein y represents a velocity of displacementbetween the rotor and the one rotor housing, u represents a controlforce, ΣY^(R) _(y) represents a sum of rotor transfer functions atrespective degrees of freedom, and ΣY^(H) _(y) represents a sum of onerotor housing member transfer functions at respective degrees offreedom; and repositioning each of the plurality of rotors to apredetermined position within the respective rotor housing by applyingthe control force to the rotor via the actuator.
 17. The method of claim16, wherein the connecting the one rotor housing to a spacecraft bymounting the one rotor housing to an isolation subsystem at all axes ofstructural communication between the one rotor housing and the isolationsubsystem while preventing structural communication from the one rotorhousing to the spacecraft further comprises: substantially limitingdisturbance forces that occur at frequencies higher than a predeterminedrate from communicating with the actuator by a damper element within theisolation subsystem; and permitting attitude control forces that occurat frequencies lower than the predetermined rate to communicate with theactuator by a voice coil within the isolation subsystem.
 18. A method ofdecoupling a rotor housing from a spacecraft by mounting the rotorhousing to the spacecraft via a D-strut hexapod that is softer than thespacecraft, that is softer than the rotor housing and that preventsdisturbance forces of the rotor housing from entering the spacecraft.